Content The course introduces information theory, network theory and game theory to characterise and model systems that cannot be treated with the fully ordered or unordered interaction models of statistical physics. A perfect magnet or an ideal gas consists of indistinguishable parts that interact without intentions in completely ordered or disordered structures. Few interesting systems in nature can be described with such simple models. Social and economic systems often consist of unique elements that interact with specific intentions and exchange information in complex structures. But just as for simple systems such as magnets and gases, the key to understanding social and economic systems is to link microscopic descriptions with macroscopic phenomena.
By combining basic knowledge and understanding within information theory, network theory, and game theory, we derive simple models to understand the fundamental mechanisms of aggregate behaviour in markets. Starting with the concept of entropy, we derive basic concepts in information theory in order to mathematically describe the important role of information in social and economic systems. The network part of the course addresses crucial effects that arise because the interaction patterns are often neither fully ordered nor completely unordered. The game theory part deals with mathematics to describe situations when the outcome of interactions between different individuals depends on the intentions or strategies of each individual.
-How to play optimally given a specific odds? -How can it pay-off to act unselfishly? -How does the design of an auction affect the result? -How does the position in a network influence strategies and outcomes in negotiation?
The course comprises a theory part of 5.0 credits and a project part of 2.5 credits.
Expected study results To fulfil the goals of knowledge and understanding, the student should be able to:
describe and apply basic concepts, relationships and methods in information theory, such as the relationship between:
- entropy and information, - entropy and the limit for maximum data compression, - data compression and optimal gaming,
describe and apply basic concepts and methods in network theory, such as:
- strong and weak links, group structure and network dynamics, - network effects and information spreading on networks, - analysis and modelling of the structure of large-scale information networks,
describe and apply basic concepts and methods in game theory, such as:
- simple games with and without interactions and the relationship between Nash and evolution equilibrium, - how rules, conventions and mechanisms of a market affect how individuals use and aggregate information, - how voting systems affect how individuals aggregate information and make a joint decision.
In order to fulfil the goals for proficiency and ability, the student should be able to:
demonstrate the ability to work towards a well-defined goal in a project using a project management model in groups of at least four people,
analyse a problem or system within one or more of the subject areas of information theory, network theory and game theory;
demonstrate the ability to collect, present and apply the necessary knowledge jointly in a group to solve the problem.
In order to fulfil the goals for values and critical approach, the student should be able to:
evaluate different solutions to problems in one or more of the subject areas of information theory, network theory and game theory;
reflect on their efforts in project work,
assess the quality of the group's results and give suggestions on how the results could be improved.
Forms of instruction The teaching is conducted in the form of lectures, exercises, hand-in assignments and supervision in a larger project. Assignments and project work are compulsory elements of the course.
Examination The examination of the course is in the form of oral and written reports of hand-in problems and a project, and an individual oral exam at the end of the course.
Eligibility - A first programming course in either C or Python, in both cases including Matlab. - A first course on statistics. - Classical Mechanics. Please also refer to the official "Required Knowledge".
Literature Networks, crowds, and markets: reasoning about a highly connected world Easley David., Kleinberg Jon. New York : Cambridge University Press : 2010. : xv, 727 p. : ISBN: 978-0-521-19533-1 (hardback)